David Cameron has launched a highly personal attack on Jeremy Corbyn by saying that his mother would expect the Labour leader to wear a proper suit, do up his tie and sing the national anthem.

The prime minister made the remarks after a Labour MP shouted out in the Commons chamber that Mary Cameron should be asked about the NHS after she signed a petition opposing cuts to children’s centres.

The prime minister replied: “Ask my mother? I think I know what my mother would say. I think she’d look across the dispatch box and she’d say: put on a proper suit, do up your tie and sing the national anthem.”

Corbyn immediately hit back and cited his late mother, Naomi, a peace campaigner. He said: “Talking of motherly advice, my late mother would have said: ‘stand up for the principle of a health service free at the point of use’ because that is what she dedicated her life to, as did many people of her generation.”

The prime minister’s comments marked a new low in his attacks on Corbyn. Until now the prime minister has focused on what he regards as the folly of the Labour leader’s political beliefs, ranging from his support for unilateral nuclear disarmament to his equivocal response to questions about what the security forces should do in the event of a Bataclan-style attack in Britain.

But the prime minister believes that his mother, a retired magistrate, speaks for middle Britain in believing that a mainstream political leader needs to wear a sharp suit and tie. Corbyn’s trousers are invariably baggy and his shirts can be ill-fitting.

Cameron rounded off his personal attack on Corbyn with a new flank in his political attack, as he highlighted the appointment of Damian McBride, who was forced to resign as Gordon Brown’s former communications director after offering support for a website that would have launched personal attacks on Tories, as an adviser to the shadow defence secretary, Emily Thornberry.

The prime minister said: “To be fair to the Labour party, they have got an answer [on defence]. They’re not going to spend 2%, they’re not going to renew our Trident submarines, but they come up with a really brilliant answer. They are bringing back, as their spokesman and spin doctor, Damian McBride six months after saying: ‘We can win in 2020 but only if we spend the next five years building this movement and putting forward a vision for the new kind of politics – honest, kinder and more caring’. Six months on Damian McBride is back. That says it all.”

The criticisms of Corbyn’s attire came as the two leaders engaged in testy exchanges on the NHS, during which they both sought to claim the mantle of Nye Bevan. The prime minister said Labour’s postwar minister for health, who founded the NHS, would support the government’s manifesto pledge to provide a consistent service across the health service.

Cameron said: “I think if Nye Bevan was here today he’d want a seven-day NHS because he knew the NHS was for patients up and down our country.”

Corbyn replied: “Nye Bevan would be turning in his grave if he could hear the prime minister’s attitude towards the NHS. He was a man with vision who wanted a health service for the good of all.”

The Labour leader had earlier accused the government of using “misrepresented research” to show an increase in mortality rates over the weekend. Corbyn quoted the authors of a report cited by the prime minister and the health secretary, Jeremy Hunt. The report, published in the British Medical Journal last year, highlighted the fact that more deaths occur within 30 days of admission to hospitals between Fridays and Mondays. Corbyn said the authors had said it was rash and misleading to say the deaths are avoidable.

The prime minister, who accused the British Medical Association of promoting inaccurate statistics in a campaign of scaremongering, used a sleight of hand to wrongfoot Corbyn. The prime minister said it was wrong to accuse the health secretary of saying there were 6,000 excess deaths at weekends, because the actual figure was 11,000 “now we have had time to go into these figures in more detail”. The revision of the figures was made last year and the point raised by Corbyn still stood – that the authors of the report say it is not possible to say if the deaths could be avoided.